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On \(q\)-steepest descent method for unconstrained multiobjective optimization problems. (English) Zbl 1484.90101

Summary: The \(q\)-gradient is the generalization of the gradient based on the \(q\)-derivative. The \(q\)-version of the steepest descent method for unconstrained multiobjective optimization problems is constructed and recovered to the classical one as \(q\) equals 1. In this method, the search process moves step by step from global at the beginning to particularly neighborhood at last. This method does not depend upon a starting point. The proposed algorithm for finding critical points is verified in the numerical examples.

MSC:

90C29 Multi-objective and goal programming
05A30 \(q\)-calculus and related topics
90C52 Methods of reduced gradient type
90C53 Methods of quasi-Newton type

Software:

OLAF; qFunctions
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Full Text: DOI

References:

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